# The wonderful physics of heat exchangers

• I will always be grateful to Rossi and Wong for encouraging me to learn about heat exchangers. The maths, which I had when young always avoided as being unpleasantly messy, is in fact remarkably beautiful. And the engineering trade-offs behind the device which Rossi told Wong he used are fascinating. It is those, not properly debated anywhere yet, that I thought might be of interest. Academic only, now the Trial is cancelled.

The background (for those new here) is that Rossi needed to find a way to dispose of 1MW of claimed heat from his claimed 1MW power plant in the IH long-term test. Otherwise, IH experts argued convincingly, the factory would have overheated. Rossi and his expert appeared to accept this in depositions. Rossi's expert explained how a heat exchanger no longer present, which Rossi had described to him, would be sufficient to blow 1MW (in fact Wong calculated 1.4MW) of heat out of an upstairs window.

I realise that not everyone here will be as interested in these details as me, but I'm sure some will. For those who just want the conclusions, they are as follows. The first few are old material, recapped here for those new to the story:

• The Wong calculations for heat exchangers depend on the total surface area of tubing, the temperatures of piping (to be cooled) and flow rate of air (doing the cooling) and the heat transfer coefficient (HTC) which shows how effective is the tube surface, on average, at dissipating heat.
• Wong uses a fixed HTC which he quotes from a source in the text of his report.
• If Wong's HTC is correct then, even though his calculation is ball-park, it shows the heat exchanger to be of the right size to dissipate 1MW. The air coming out of that window would be very hot, close to 100C, thereby reducing the exchanger efficiency. Nevertheless most of that 1MW could be so dissipated.

When presented with these calculations my first thought was to question the HTC. Although indeed a number of internet references agree with Wong about this, it is very vague. It is pretty obvious that HTC should vary with wind velocity (sort of 101 of heat exchanger theory). Wong ignores this, using the value quoted for moderate velocity. And, anyway, I suspected this convenient figure to come not from Wong but from Rossi, because the reference was unusually for Wong's references a non-English-language one and appeared to be Italian. Maybe the value was being misused?

The first thing to do was to track down Wong's reference:

Overall heat transmission coefficient between moderate air cross flow and carbon 1.5 steel. See [OPPO Conductibita Termica] The value is 200W/m2C.

to see the figure in its real context. The reference is difficult to track down. Unlike all Wong's other references (properly stated in a bibliography) this is added into the report text as an off-hand remark. It is from an Italian web-site which however does not anywhere provide this data - although it does tabulate a vast amount of similar engineering data, specifically it shows the thermal conductivity coefficients for many materials. Other web references give this figure but with very vague context: it seems to be an internet myth.

So then I went to source material to determine how HTCs are calculated. Basically, there are two dimensionless numbers that determine the HTC: Nusselt number describes the gas characteristics (viscosity, density, specific heat capacity). For air it varies with temperature relatively little, and can easily be computed for the relevant temperature here of 50C or so. The Reynolds number describes the speed of flow relative to the typical dimensions of the problem (the diameter of the pipe) and the time of the interaction. It determines how turbulent is the flow. It can be easily worked out from the air velocity and the tube diameter. The HTC dependence on Reynolds number is complex and non-analytic. Various approximate formula are available each correct within different ranges of Reynolds Number. I looked at several and for the problem here they agree.

I constructed a spreadsheet (see attachment for this with some things added as noted later) that would work out HTC (and then using Wong's simple formula the overall dissipation) from the pipe diameter - fixed and given by Rossi - the pipe length (the same) and the air flow velocity and total flow. Total flow rate is fixed by the fans and given by Wong from information provided by Rossi. Velocity is not given by Rossi and must be determined.

Wong's value of 200W/m^2C requires an insanely high wind speed over the tubes. 75m/s or Hurricane cat 1. The reason for such high speed is that large tubes (as Rossi used) give lower HTCs than small tubes. The internet myth figure is possible at reasonable speeds but only for very thin tubing as for example in a vehicle radiator.

Even de-rating by 1/3 to give 500kW total diSsipation requires a high wind speed of 20m/s or force 8 gale.

Can Rossi's fans deliver this high wind speed? this depends on the area they are blowing wind through. For a given air flow the smaller the area the higher the speed. But the air must blow over all the tubes. If the area of the passage through which it blows is small, it must move multiple times over each tube.

This is a standard construction for heat exchangers using baffles. They force the air to move across the hot rods in multiple separate boxes. At the end of each box there is a passage way through to the next box, inside which the air blows across the same tubes in the opposite direction.

To get the 20m/s 500kW speed we need to have 10 separate boxes to run the air 10X over the tubes. That reduces the flow area by 10X, and speeds up the velocity from 2m/s to 20m/s as needed.

Such a design is just about defensible. So it looks as though Wong is right?

Power it up, Scottie!

In fact as intuition would tell you (1MW heat exchangers are big beasts) Wong was wrong. But his calculations are all justifiable. The weird HTC does not matter because (as he would know) you can get whatever HTC you want by varying wind speed and you can make speed arbitrarily high by increasing the number of baffles.

So what is the engineering trade-off? Why can we not make small cheap heat exchangers this way just by having a very large number of baffles?

It turns out that the key problem is the power needed to push the air through the heat exchanger. Obviously, the faster it moves, the more drag you get and the more power is needed. Also, whenever the air changes direction, power is lost due to the turbulence in the momentum change, though that is difficult to quantify. I used standard calculations for the air pressure drop over tubes. There are 22 tubes in Rossi's design. But if the air criss-crosses them 10 X the total drag is as from 220 tubes. You can see the trade-off here. As the number of baffles increases so the drag increases at a very fast rate from two separate effects. The number of tubes the airflow crosses increases (linear) and the wind velocity and hence turbulence also increases (faster than linear).

I added this into the spreadsheet - attached to this post - and modelled the airflow fan back-pressure due to the air speed and the total drag on the air as a function of the number of baffles.

As the number increases so does the heat exchanger power dissipation, but also the necessary air pressure. it is easy to compute the mechanical power output of the fans, and hence their electrical input. For even 500kW dissipation, 3X lower than Wong's suggestion, the total power output by the heat exchanger fans is much larger than the total power drawn from the FPL supply!

Those with access to specialised heat exchanger design tools could repeat this modelling - perhaps with more accuracy. I'm confident that my results are correct to within 30% or so, and the proposed design is so far from possible even de-rated to 500kW that I'm confident it could not have done what Rossi claims.

Most here won't be interested because they believe the heat exchanger to be fictional. So do I. What I find interesting is how a superficial theoretical analysis of a real possible product (Wong) can leave out the actual trade-offs and generate totally unrealistic conclusions.

Wong HTC reference - the details

The word Conductibita does not translate to English, although Termica is Italian for Thermal, and it seems likely that Conductibita is meant to mean Conductivity. This title does not exist on the web.

Wong’s background is not Italian and I find the insertion of an Italian reference here weird, especially when he gives as the reference he used for Heat Exchangers (the topic here) a perfectly good reference from which the exact value of h could easily be derived (more later on that).

The Italian for Thermal Conductivity is Conduttività Termica and this appears to be what Wong meant. From this and the word OPPO we find a web reference page of data, etc, which is certainly the reference he meant:

http://www.oppo.it/tabelle/conducibilita_termica.htm

This unfortunately does not give the coefficient Wong claims to have found here. It gives thermal conductivity of mild steel (something quite different, and has no value any where near what is stated). Nor do any other pages under the OPPO site give the required coefficient. In any case Wong would need to translate this Italian site to read it. My view is that Rossi gave Wong this coefficient, and this incorrect reference from a site with data but not the required data. The figure he uses is a RossiSays!

The value used 200W/m2K is however found in many other places on the web with the vague definition close to what Wong uses. It is a typical value for any surface – not as Wong states specific to mild steel. (In this case the surface has no effect on the answer. Roughness matters but not as much as other things). So as with all Rossisays the stated figure has some loose resemblance to fact. For example:

http://thermopedia.com/content/660/

This typical value is ill-defined and not found in serious books on Heat Exchangers. I can nowhere find a definition of precisely what it means. Thus: what is moderate air flow? What size pipe (both air flow rate and pipe diameter make a big difference) does the value apply to? It appears to be a web myth copied from one place to another with original source lost. Note that many web sites supply the correct, precise equation used to calculate the correct figure:

http://www.engineersedge.com/h…_air_convection_13963.htm

Calculations - details

See the enclosed spreadsheet. I have not given a good explanation for the numbers and formulae (though there is some). I'll answer questions if anyone is interested.

## Files

• htc-calcs2.zip

• Ever since reading the heat exchanger description in the Wong report, I wondered about the supposed exchanger. If I would have designed the heat exchanger, I would have bought a cheap used exchanger from an industrial plant. (Industrial plants often sell old exchangers for next to nothing because it costs a fair amount of money to dispose of them. This way they get a minor amount of money instead of spending money.) After refurbishing, I would have piped the steam as input and cooled it with water from the city, then sparged both lines back into the reactor supply. To me, this would have made the most efficient use of power. Not having an engineering background, I have a question about this setup. Given one megawatt of steam, would you still have to have a cooling tower in my setup or would the natural heat loss been enough to dissipate the heat safely?

• I agree an industrial heat exchanger would be the way to go. You need to find a hot water in -> air out model. These are less usual since CHP plants etc all need high temp air in -> water out. It would use a significant amount of power, more than the reactors. I think you'd need to vent the 1MW as air rather than anything else, because 1MW power has got to go somewhere - and the only options are the atmosphere or the drains (as hot water).

That much hot water would be problematic because the large water flow, if possible, would be noticed by city authorities and it would be against regulations (at least I think that is true).

• I agree an industrial heat exchanger would be the way to go.

The right choice would have been an air cooled condenser...

http://www.unitedcoolingtower.…=Air%20Cooled%20condenser

or a Steam Heated Air Heater...

http://www.thermotech-finnedtu…d-Heated-Air-Heaters.html

All of them are usually made of finned tubes, in order to get a large heat exchange surface.

Of course, such finned tubes are not available at home-depot, and cannot made by hand.

And buying such a finned-tube heat exchanger should leave some records.

That's why Rossi had to came up with this stupid idea that this imaginary heat-exchanger was made of ordinary pipes, which would make a 1MW heat exchanger extremely large and heavy.

An industrial finned tube heat exchanger would be significantly smaller, but still you have to get rid of the same amount of hot air.

## Images

• Does it change the energy budget if the fans for the heat-exchanger were drawing air rather than pushing it? In his deposition, Wong seems to believe that the fans were right up against the window openings and were meant to suck air from the exchanger box and expel it directly to the outside.

• Does it change the energy budget if the fans for the heat-exchanger were drawing air rather than pushing it? In his deposition, Wong seems to believe that the fans were right up against the window openings and were meant to suck air from the exchanger box and expel it directly to the outside.

It would mean at higher pressures this just would not work, because the maximum suction available is one atmosphere. The fan power relates to the pressure difference and is no different.

But the flow rate is high. For 450kW dissipation - and fan power an impossible (given FPL data) 50kW - we have only 3kPa pressure difference or 0.03bar. So no problem.

• PS - what I'd like is for the ECW guys (and specifically E48) to read the above and answer. E48's answer to the conversation about erroneous HTC is that it would be Ok if the wind velocity was high enough, which could be got from a design with baffles. That is sort of true - though Wong left out any mention of baffles there is no requirement on him to do that. But the power argument knocks this on the head.

• Really nice Sir Huxley - I wonder everyday why such an incredible concoction would be built "inside" in the first place unless it was super-duper top trade secret magnificence like the rest of the story. And then there is the air intake - toupees wouldn't stand a chance coming in the front or back door. Very much appreciate your continued focus and work on this tale - this does all appear to be heading in a certain direction and that may be best for all concerned after all.

• Your calcs seem reasonable, and it is amusing to see the google hits for "Conductibita".

The air coming out of that window would be very hot, close to 100C

It wouldn't be... Not without a properly designed counterflow HE. With pipes arranged how Rossi describes, that isn't happening.

But that doesn't have any real repercussions on your results, it only reduces the efficiency of the supposed apparatus.

• Maybe this excel sheet could be helpful for the specialist for some calculations.

• Do people really still use imperial units?

• It wouldn't be... Not without a properly designed counterflow HE. With pipes arranged how Rossi describes, that isn't happening.

But that doesn't have any real repercussions on your results, it only reduces the efficiency of the supposed apparatus.

Hi Zeuss,

Can you explain this? I think you are wrong because the limitation here is the temperature of the air on exit.

The air on exit from the heat exchanger must be around 100C (or with the stated fixed flowrate it cannot hold the required power). So however you slice it this means that at the exit the pipes are much less efficient. A good approximation is that for 1MW dissipated the average temperature difference is 50% of what it would be at low powers where the air is not much heated up.

As you say though this question does not really alter the conclusions even if you were correct. At 500kW (which I've been working to, on the grounds that maybe you could manage 500kW dissipated through walls and ceiling of a big warehouse)

On a separate issue...

Rossi's comment about sunlight on the roof is as usual superficially clever and completely wrong. A roof will get very hot in sunlight even though it is able to radiate and convect into open cold air. Luckily in this case the downward HTC (from roof to inside air) is smaller so that a hot roof does not lead to such hot air inside.

For heat inside a building, even with no insulation in the roof, there are two steps. The inside air heats up the roof, which only then loses heat via external convection. We can calculate heat loss form downward convection from air in room to roof. and upwards convection from roof to outer air, both of which are in series so you get less loss than for just one. You can find typical badly insulated roof U values, solving this, in many places, 2.5W/m^2K looks about right (and any roof insulation makes things much worse).

So for a 10C difference between indoor and outdoor air (making the factory unlivable on a hot Florida Summer day) we have around 25W/m^2 dissipation. Compare this with total solar radiation at surface of around 1000W/m^w and you can see how Rossi has over-estimated this effect by a factor of 40.

1 MW would require 50,000 m^2 (500,000 sq feet) of roof. Rossi does not have that much. Anyone remember the exact roof area? I did a rough U value calculation for the whole factory at one point (I now cannot remember what dimensions I used) and 1MW was very unlivable.

• Can you explain this? I think you are wrong because the limitation here is the temperature of the air on exit.

Basically you can't make a counterflow heat exchanger if the pipe is snaking back and forth... which end is the hot end, and which is the cold end?

The diagram at the top of this page may explain this a bit better... only a counterflow HE can approach a 100% temperature match, (ie. 100% efficiency) assuming the parameters are optimised. https://www.quora.com/Why-is-a…allel-flow-heat-exchanger

The air on exit from the heat exchanger must be around 100C

It could be less (I argue 'must be'), but one would have to blow more air over the pipes to balance everything.

Rossi's comment about sunlight on the roof is as usual superficially clever and completely wrong. A roof will get very hot in sunlight even though it is able to radiate and convect into open cold air.

I like to think of it as: If the sun's 1MW heated the roof from 0K to 310ish... What's another 1MW going to do?

At 500kW (which I've been working to, on the grounds that maybe you could manage 500kW dissipated through walls and ceiling of a big warehouse)

Yeah that's approximately the same as I worked it out to be... fag packet style. Probably a bit higher actually... IIRC about 350-450kW unventilated. Although it would need to be noticeably hot inside the building to transmit that much.

The post was edited 1 time, last by Zeus46 ().

• I've just found Rossi's comment on Mats' blog - so unpleasantly accepting of Rossi untruths it is annoying to read.

Anyway Rossi says 1000m^2. That means approx 25kW exits through the roof with the near-roof air +10C from outside. (2.5W/m^2K can be validated intuitively as follows. A single-glazed glass window, for example, gives 5W/m^2K and therefore would allow 50kW from this temperature difference. Obviously any roof will be more insulated than a single 12mm pane of glass).

• OK: guestimated dimensions: 15m X 75m X 6m high.

Allow U value 2.5W/m^2 all walls and roof and floor. Total of 180+450+1100 sq m = 1750 sq m. => +10C -> 45kW.

So max 500kW dissipated through walls, floor, open windows, went fans, etc looks safe, I'd expect a more accurate estimate < 200kW.

• So max 500kW dissipated through walls, floor, open windows, went fans, etc looks safe, I'd expect a more accurate estimate < 200kW.

Are you saying this is approximately how much heat can be dissipated with an normal building, with conventional HVAC? I think it is less than this. Two real-world examples:

The average U.S. movie theater capacity is 200 to 300 people. 300 people generate ~30 kW of heat. A rented theater crammed with a standing only crowd for something like a political rally gets hot. In other words, ordinary theaters cannot handle much more than ~30 kW.

A commercial kitchen stove and oven produces 60,000 btu, 30 kW. You are not allowed to install one without extra HVAC ventilation: a hood. The hood is there to remove smoke, but I think without extra ventilation, one or two stoves (120 kW) in a small restaurant would make the whole building intolerably hot. A commercial kitchen is uncomfortably hot even with the ventilation equipment.

• People in movie theatres are unlikely to tolerate an extra 10C above the outdoor temperature...

• People in movie theatres are unlikely to tolerate an extra 10C above the outdoor temperature...

You are missing the point. I am talking about the HVAC systems, not the people. The HVAC cannot cope with much more than 30 kW. They are not designed for higher power levels. 100 or 200 kW would completely overwhelm them.

• FALSE !

you can easily find commercial HVAC system of 1MW power:

http://www.emersonclimate.com/…or_systems_up_to_1MW.aspx

As usual Jed you pretend to be expert of everything but you are not even able to make an internet search.

As usual Ele you are missing the point.

The link describes a heat pump with 1MW cooling at 150kW power in. You will note that for Rossi's heat exchanger any power used, unless very small, is quite impossible due to the fact that the FPL power figures and the ecat power in figures match.

Hence Rossi's heat exchanger is just not possible.

• The word Conductibita does not translate to English, although Termica is Italian for Thermal, and itseems likely that Conductibita ismeant to mean Conductivity. This title does not exist on the web.

What you are not able to translate Conducibilità Termica ? Is simply "Thermal conductivity"

and again Voilà a nice table in Italian searched as Conducibilità Termica http://fisicatecnica.altervista.org/tabelle/tab_conduc.htm

ans of course in english:

https://www.nde-ed.org/Educati…l/ThermalConductivity.htm

THH, as for children : Shame on you ! you are not able to use google translator and google !

• I've just realised.

Ele - read what I said? The reference was Conductibita which is not a word. However, as you would note if you had read my post, I reckoned Wong meant Conductibilita. He must have written down what Rossi gave him wrong.

The mystery though is why did Rossi give this site as a reference when it does not have the relevant coefficient? Note that neither your table nor the referenced OPPO site has the relevant isothermal rod to forced air figure.

• The link describes a heat pump with 1MW cooling at 150kW power in. You will note that for Rossi's heat exchanger any power used, unless very small, is quite impossible due to the fact that the FPL power figures and the ecat power in figures match.

Hence Rossi's heat exchanger is just not possible.

THH if I produce 1MW of heat + 20kW what I have to dissipate is just 1.02MW . Just that ! 1MW cooling wil do.

My searches were very quick and demonstrate that you are just building a "Card castle" without any ground.

As usual the thesis here "IH had not sufficient experts, we are much better of anybody".

But if that was so evident why you have not gone to court to testify ?

Probably, you are the first that knows that what you are saying is false and you would not able to repeat it under oath !

• I reckoned Wong meant Conductibilita.

Even Conductibilita is not a word. The real one is Conducibilità.

• The mystery though is why did Rossi give this site as a reference when it does not have the relevant coefficient?

Is just one of the many sites and references. Conductivity is a property of materials and has nothing to do with forced air.

Regarding forced air the term Heat Tranfer is used:

• 300 people generate ~30 kW of heat.

Yes internally and you of course ignore heat coming from ambient (external sun light on the building, weather conditions ecc...) that can rise that figure. Sun delivers approximately 1kW of heat per square meter of surface so 1MW on 100 square meters = 10763.9 square foot that is approximately the area for a 600 seats theater.

• You are missing the point. I am talking about the HVAC systems, not the people. The HVAC cannot cope with much more than 30 kW. They are not designed for higher power levels. 100 or 200 kW would completely overwhelm them.

A person dancing (to techno or similar) produces 300W heat.

200 gurning ravers can produce around 60kW in a 12x12m area, and that's just a small club... Imagine a 2000 capacity venue... The HVAC works fine.... It has to.

The post was edited 1 time, last by Zeus46 ().

• A simple internet search and voilà a 1MW heat exchanger just abou 2meters long !

But fortunately Bowman aren't absurd enough to make their heat exchangers out of 6 inch wide piping.

• And come to think of it... It seems Rossi can't use the internet either... Why weld hundreds of metres of pipe together when he could have got an off-the-shelf solution from Bowman???

Answer: Because buying from Bowman would have left a paper trail, which would have necessitated faking the documents when Rossi realised post-fact that he needed a heat exchanger. Far too risky when a simple phonecall to Bowman would have exposed him.

(Based on steel price and site-welding costs, I reckon a Bowman heat exchanger would have probably worked out much, much cheaper)